Equilibrium models of differentially-rotating polytropic cylinders

The equilibrium structure of differentially rotating polytropic cylinders is determined numerically. We setn=3 and use a quadratic function for the law of differential rotation. We construct different models by varying the angular velocity at the axis and the ratio of the angular velocity at the surface to the angular velocity at the axis. By taking a decreasing function for the rotation law we are able to treat models with an angular velocity at the axis greater than the break-up velocity of uniformly rotating cylinders. We also determine whether a Richardson-like criterion for stability is violated in the models.     

Meridian circulation in differentially rotating stars

We formulate the first order theory of meridian circulation in radiative zones of approximate chemical homogeneity so as to allow calculation of circulation velocities in a star subject to an arbitrary axially symmetric angular velocity ω(r, θ). The calculation includes circulation due to perturbations in the nuclear burning rate. The formalism agrees with previous calculations relevant to special cases, and assumes maximum simplicity for rotation on cylinders. We find two types of steady state configurations: (1) rotation according to a special class of distributions ω(r, θ) which drive no currents, and (2) rotation according to arbitrary ω(r, θ), but with a correction to the molecular weight μ such that the net circulation velocity is zero. We find that a small μ gradient can quench the circulation in many cases. In particular, we conclude that a large differential rotation in the Sun might have escaped disruption by meridian currents, for a μ stratification of a few parts in 10³.     

Baroclinic instability in differentially rotating stars

A linear analysis of baroclinic instability in a stellar radiation zone with radial differential rotation is performed. The instability sets in at a very small rotation inhomogeneity, ΔΩ ～ 10^?3Ω. There are two families of unstable disturbances corresponding to Rossby waves and internal gravity waves. The instability is dynamical: its growth time is several thousand rotation periods but is short compared to the stellar evolution time. A decrease in thermal conductivity amplifies the instability. Unstable disturbances possess kinetic helicity. Magnetic field generation by the turbulence resulting from the instability is possible.     

Structure of polytropic models of stars containing poloidal magnetic fields

Polytropic models of axially-symmetric equilibrium stars of infinite conductivity with poloidal magnetic fields are constructed by numerical integration of the exact equations governing internal structure. The mathematical method used, a further generalization and improvement of Stoeckly's method, allows the construction of a sequence of equilibrium models starting with a spherically symmetric star (when no magnetic field is present) and terminating with a doughnut-shaped object (for a very strong magnetic field) — a fact already shown by Monaghan. Detailed results are given only for two polytropes with the indexn=1.5 and 3.0, although any other value ofn greater than or equal to one could have been selected. Contrary to Monaghan's results, it is found that along the sequence of configurations forn=3.0 the ratio of the magnetic and gravitational energy peaks out before a doughnut-shaped configuration is reached; but this effect does not characterize then=1.5 sequence. The calculations confirm, however, another result of Monaghan asserting that the magnetic field is a fairly insensitive function of the polytropic index.     

Effect of rotation and tidal distortions on the structure of polytropic stars

The averaging technique of Kippenhahn and Thomas has been used in conjunction with Kopal's method of evaluating various parameters on the Roche equipotentials, to determine the effects of rotation and tidal distortions on the shapes and structures of the polytropic models of the stars.     

2-D models of rapidly rotating stars

Recent observational advances in the fields of asteroseismology and interferometry, have put in evidence the need of physically realistic models of rapidly rotating stars. In rapidly rotating stars, the centrifugal force affects dramatically the structure of the star and makes it necessary to use 2-D methods that take fully into account the deformation of the star. We compute the structure of rapidly rotating stars using 2-D spectral methods. The advantage of spectral methods compared with finite difference methods is that they can achieve the same accuracy while reducing significantly the number of grid points, thus saving computing time. The models include core convection and realistic microphysics (tabulated equation of state and opacity).     

On the solution space of differentially rotating neutron stars in general relativity

A highly accurate, multidomain spectral code is used in order to construct sequences of general relativistic, differentially rotating neutron stars in axisymmetry and stationarity. For bodies with a spheroidal topology and a homogeneous or an   N = 1  polytropic equation of state, we investigate the solution space corresponding to broad ranges of degree of differential rotation and stellar densities. In particular, starting from static and spherical configurations, we analyse the changes of the corresponding surface shapes as the rate of rotation is increased. For a sufficiently weak degree of differential rotation, the sequences terminate at a mass-shedding limit, while for moderate and strong rates of differential rotation they exhibit a continuous parametric transition to a regime of toroidal fluid bodies. In this article, we concentrate on the appearance of this transition, analyse in detail its occurrence and show its relevance for the calculation of astrophysical sequences. Moreover, we find that the solution space contains various types of spheroidal configurations, which were not considered in previous work, mainly due to numerical limitations.     

Pseudo-Newtonian models for the equilibrium structures of rotating relativistic stars

We obtain equilibrium solutions for rotating compact stars, including special relativistic effects. The gravity is assumed to be Newtonian, but we use the active mass density, which takes into account all energies such as the motion of the fluid, internal energy and pressure energy in addition to the rest-mass energy, in computing the gravitational potential using Poisson's equation. Such a treatment could be applicable to neutron stars with relativistic motions or a relativistic equation of state. We applied Hachisu's self-consistent field (SCF) method to find spheroidal as well as toroidal sequences of equilibrium solutions. Our solutions show better agreement with general relativistic solutions than the Newtonian relativistic hydrodynamic approach, which does not take into account the active mass. Physical quantities such as the peak density and equatorial radii in our solutions agree with the general relativistic ones to within 5 per cent. Therefore our approach can be used as a simple alternative to the fully relativistic one when a large number of model calculations is necessary, as it requires much fewer computational resources.     

Gravity modes in composite polytropic stars

We study gravity modes of composite polytropic stars which consist of two convectively stable zones separated by a convectively unstable zone. In addition to the unstable gravity modes associated with the intermediate zone, we distinguish two types of stable gravity modes, one type being mainly associated with the core, the other one being mainly associated with the envelope. We find also some accidental resonances between the core and the envelope.     

Physical characteristics of critically distorted or almost spherically shaped rotating magnetic polytropic models

We use the so-called complex plane iterative technique (CIT) to the computation of polytropic stars distorted by rotation (either rigid or differential) and magnetic fields (both toroidal and poloidal). We give emphasis on computing(i) critically rotating configurations, and (ii) configurations that – dueto the counterbalancing of the effects of rotation and poloidal magnetic field with the effects of toroidal magnetic field – obtain an almost spherical shape. This revised version was published online in July 2006 with corrections to the Cover Date.     

Thermal structure of the envelopes of rapidly rotating neutron stars

For a neutron star which rotates like the fastest millisecond pulsar we calculate the temperature profile within the envelope. We find a small decrease of the surface temperature and a considerable increase of the thickness of the liquid layer from the pole to the equator.     

On secular stability of rapidly rotating stars of arbitrary structure

The aim of the present paper will be to utilize Poincaré's criteria to investigate secular stability of self-gravitating configurations, of arbitrary structure, in the state of rapid rotation. The potential energy, a knowledge of which is necessary for application of these criteria, will be determined by an extension of Clairaut's method; and its evaluation in terms of suitably chosen generalized coordinates carried out explicitly to quantities of fourth order in superficial oblateness, for configurations of arbitrary internal structure.The method employed can, moreover, clearly be extended to attain accuracy of any order — at the expense of mere manipulative work which lends itself to machine automation; and the angular velocity of axial rotation can be an arbitrary function of position as well as of the time. An application of our results to homogeneous configurations in rigig-body rotation will be undertaken to demonstrate that our method, when applied to a case for which a closed solution exists, leads to results which are consistent with it.     

Equilibrium structure of stars obeying a generalized differential rotation law

In the present paper we have considered the problem of determining the equilibrium structure of differentially rotating stars in which the angular velocity of rotation varies both along the axis of rotation and in directions perpendicular to it. For this purpose, a generalized law of differential rotation of the type ² =b ₀+b ₁ s ²+b ₂ s ⁴+b ₃ z ²+b ₄ z ⁴+b ₅ z ² s ² (here is a nondimensional measure of the angular velocity of a fluid element distants from the axis of rotation andz from the plane through the centre of the star perpendicular to the axis of rotation, andb's are suitably chosen parameters) has been used. Whereas Kippenhahn and Thomas averaging approach has been used to incorporate the rotational effects in the stellar structure equations, Kopal's results on Roche equipotentials have been used to obtain the explicit form of the stellar structure equations, which incorporate the rotational effects up to second order of smallness in the distortion parameters. The method has been used to compute the equilibrium structure of certain differentially rotating polytropes. Certain differentially rotating polytropes. Certain differentially rotating models of the Sun have also been computed by using this approach.     

Effects of rotation and tidal distortion on the periods of small adiabatic oscillations of the polytropic models of the stars

The averaging technique of Kippenhahn and Thomas (1970) has been used in conjunction with Kopal's method of evaluating various parameters on the Roche equipotentials to determine the effects of rotation and tidal distortions on the periods of small adiabatic radial and nonradial modes of oscillations of polytropic models of the stars.     

The structure of rotating stars from an extension of the Kippenhahn-Thomas method

A method is presented whereby the structure of rotating stars may be determined from an initial guess at the geometry of equipotential surfaces. The method may be considered an extension of the work of Kippenhahn and Thomas in that a uniformly continuous geometry is defined in terms of the appropriate spherical model with Roche characteristics at the surface of the configuration and sphericity at the centre. A simple Cowling model in uniform rotation is employed to illustrate the technique and for comparison purposes with previous work.